Conformal mapping onto the exterior of a regular triangle

Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, Джаксыбаев, Султанбек Амангельдиевич

Ilim ha’m ja’miyet · 2026-yil

Annotatsiya

This article considers the conformal mapping of the exterior of the unit disk (the domain |z|>1) onto the exterior (unbounded) domain of a regular triangle. The mapping function is derived using the exterior form of the Christoffel–Schwarz integral, expanded into a power series, and its properties are analysed. It is shown that the logarithmic capacity (conformal radius) of the triangle is expressed through the transcendental constant Γ(1/3): R/C = 2/3 B(2/3,2/3) = 8π²/3Γ(1/3)³ ≈ 1.3689. As a physical application, the ideal fluid flow past the triangle is illustrated. The study employs methods of the geometric theory of functions of a complex variable, the Christoffel–Schwarz integral, series expansion, and computer visualization.

Maqola ma’lumotlari
MualliflarKalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, Джаксыбаев, Султанбек Амангельдиевич
JurnalIlim ha’m ja’miyet
NashriyotНукус давлат педагогика институти
ISSN2010-720x, 2181-1555
Nashr sanasi2026-08-15
Son5-1
Betlar9-11
Tilkaa
Ilmiy sohaFizika-matematika
Indeksga qo‘shilgan2026-08-26

Maqolaning asl sahifasi

Kalit so‘zlar

konform akslantirish, Kristoffel-Shvars integrali, muntazam uchburchak, sohaning tashqi ko‘rinishi, logarifmik sig‘im, konform radius, transfinit diametr, gamma-funksiya, kompleks tekislik, ideal suyuqlik oqimi, potensial nazariyasi, конформное отображение, интеграл Кристоффеля–Шварца, правильный треугольник, внешность области, логарифмическая ёмкость, конформный радиус, трансфинитный диаметр, гамма-функция, комплексная плоскость, течение идеальной жидкости, теория потенциала, conformal represcuting, Christoffel–Schwarz integral, regular triangle, exterior domain, logarithmic capacity, conformal radius, transfinite diameter, gamma function, complex plane, ideal fluid flow, potential theory

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAKalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, & Джаксыбаев, Султанбек Амангельдиевич (2026). CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE. Ilim ha’m ja’miyet, (5-1), 9-11. https://journal.ndpi.uz/index/article/view/2026-5-1-003
GOST (OAK)Kalbaev, Sultanbek Nazerbaevich va b. CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE // Ilim ha’m ja’miyet. – 2026. – № 5-1. – B. 9-11.
MLAKalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, and Джаксыбаев, Султанбек Амангельдиевич. “CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE.” Ilim ha’m ja’miyet, (5-1), 9-11, 2026. https://journal.ndpi.uz/index/article/view/2026-5-1-003
ChicagoKalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, and Джаксыбаев, Султанбек Амангельдиевич. “CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE.” Ilim ha’m ja’miyet, (5-1), 9-11 (2026). https://journal.ndpi.uz/index/article/view/2026-5-1-003
HarvardKalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, and Джаксыбаев, Султанбек Амангельдиевич (2026) ‘CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE’, Ilim ha’m ja’miyet, (5-1), 9-11. https://journal.ndpi.uz/index/article/view/2026-5-1-003
BibTeX
@article{kalbaevsultanbeknazerbaevich2026,
  title = {CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE},
  author = {Kalbaev, Sultanbek Nazerbaevich and Jaksibaev, Sultanbek Amangeldi ulı and Kalbaev, Sultanbek Nazerbaevich and Jaksibaev, Sultanbek Amangeldi ulı and Калбаев, Султанбек Назербаевич and Джаксыбаев, Султанбек Амангельдиевич},
  journal = {Ilim ha’m ja’miyet},
  year = {2026},
  number = {5-1},
  pages = {9-11},
  url = {https://journal.ndpi.uz/index/article/view/2026-5-1-003}
}

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